
where \(L\)  is the depth of the network, \(\phi _l\)  is its feature map up to the \(l\) -th layer, and \(\lbrace \alpha _l\rbrace _{l=1}^L\)  are some constants that weigh the contributions of the \(\operatorname{\mathbf {\ell }}_2\)  distances between activations. There are two crucial elements in LPIPS: the learned network and learned coefficients \(\lbrace \alpha _l\rbrace _{l=1}^L\) . [1]} propose to take a network pre-trained on ImageNet and learn coefficients on their collected dataset of human judgemenets about which images are closer to each other.
Both [1]} and [3]} argue about better suitability of LPIPS to measure image similarity. In App.  we analyse the suitability of LPIPS over \(\operatorname{\mathbf {\ell }}_2\)  specifically on the images from CIFAR-10-C with a detailed breakdown over corruption types. In particular, we show that the LPIPS distance is better correlated with the error rate of the network, and the increase over severity levels is more monotonic compared to \(\operatorname{\mathbf {\ell }}_2\)  as can be also seen in Fig. REF .
